Surveys of some areas of recent progress in functional analysis are given and related new results are presented. The topics covered in this volume supplement the discussion of modern functional analysis in the previous Proceedings volumes. Together with the previous volumes, the reader obtains a good impression of many aspects of present-day functional analysis and its applications. Parts of this volume can be used profitably in advanced seminars and courses in functional analysis.
This volume comprises six chapters and begins by presenting some background material, such as differential-geometric sources, sources in mathematical physics, and sources from the calculus of variations, before delving into the subject of nonlinear operators. The following chapters then discuss local analysis of a single mapping and parameter dependent perturbation phenomena before going into analysis in the large. The final chapters conclude the collection with a discussion of global theories for general nonlinear operators and critical point theory for gradient mappings.
This book will be of interest to practitioners in the fields of mathematics and physics, and to those with interest in conventional linear functional analysis and ordinary and partial differential equations.
the unsteady aerodynamic flow and the finite element model for the structure. Much of the aeroelasticity has been developed with applications formerly in mind because of its enormous consequences for the safety of aircraft.
Aeroelastic instabilities such as divergence and flutter and aeroelastic responses to gusts can pose a significant hazard to the aircraft and impact its performance. Yet, it is now recognized that
there are many other physical phenomena that have similar characteristics ranging from flows around flexible tall buildings and long span bridges, alternate energy sources such as electric power generation by smart structures to flows internal to the human body.
From the foreword:
"For the theorist and applied mathematician who wishes an introduction to this fascinating subject as well as for the experienced aeroelastician who is open to new challenges and a fresh viewpoint,
this book and its author have much to offer the reader."
Earl Dowell, Duke University, USA
The book is intended for research scientists and engineers working in the fields of physics and engineering, as well as graduate students and advanced undergraduates of the related fields.
Qing-Ming Tan is a former Professor at the Institute of Mechanics, the Chinese Academy of Sciences, China.
With the inclusion of many illustrative examples and exercises, An Introductory Course in Functional Analysis equips the reader to apply the theory and to master its subtleties. It is therefore well-suited as a textbook for a one- or two-semester introductory course in functional analysis or as a companion for independent study.
The product of intensive research carried out over the last ten years, this book explores for the first time in a monograph form, results that were only previously available in journal papers.
Written in a simple style, with sections and chapters following an easy, natural flow, it will be an invaluable resource for researchers in Operator Theory and Functional Analysis. The reader is assumed to be familiar with the basic notions of linear algebra, functional analysis and complex analysis.
Many important topics that are rarely presented in an accessible way to undergraduate students are included, such as unconditional convergence of series, Schauder bases for Banach spaces, the dual of lp topological isomorphisms, the Spectral Theorem, the Baire Category Theorem, and the Uniform Boundedness Principle. The text is constructed in such a way that instructors have the option whether to include more advanced topics.
Written in an appealing and accessible style, Metrics, Norms, Inner Products, and Operator Theory is suitable for independent study or as the basis for an undergraduate-level course. Instructors have several options for building a course around the text depending on the level and interests of their students.Key features:Aimed at students who have a basic knowledge of undergraduate real analysis. All of the required background material is reviewed in the first chapter.Suitable for undergraduate-level courses; no familiarity with measure theory is required.Extensive exercises complement the text and provide opportunities for learning by doing.A separate solutions manual is available for instructors via the Birkhäuser website (www.springer.com/978-3-319-65321-1). Unique text providing an undergraduate-level introduction to metrics, norms, inner products, and their associated operator theory.
The concepts and theorems of advanced calculus combined with related computational methods are essential to understanding nearly all areas of quantitative science. Analysis in Vector Spaces presents the central results of this classic subject through rigorous arguments, discussions, and examples. The book aims to cultivate not only knowledge of the major theoretical results, but also the geometric intuition needed for both mathematical problem-solving and modeling in the formal sciences.
The authors begin with an outline of key concepts, terminology, and notation and also provide a basic introduction to set theory, the properties of real numbers, and a review of linear algebra. An elegant approach to eigenvector problems and the spectral theorem sets the stage for later results on volume and integration. Subsequent chapters present the major results of differential and integral calculus of several variables as well as the theory of manifolds. Additional topical coverage includes:
Sets and functions
Normed vector spaces
First- and higher-order derivatives
Diffeomorphisms and manifolds
Integration on manifolds
Basic point set topology
Numerous examples and exercises are provided in each chapter to reinforce new concepts and to illustrate how results can be applied to additional problems. Furthermore, proofs and examples are presented in a clear style that emphasizes the underlying intuitive ideas. Counterexamples are provided throughout the book to warn against possible mistakes, and extensive appendices outline the construction of real numbers, include a fundamental result about dimension, and present general results about determinants.
Assuming only a fundamental understanding of linear algebra and single variable calculus, Analysis in Vector Spaces is an excellent book for a second course in analysis for mathematics, physics, computer science, and engineering majors at the undergraduate and graduate levels. It also serves as a valuable reference for further study in any discipline that requires a firm understanding of mathematical techniques and concepts.
Surveys are provided on: Basic theory of fuzzy metric and normed spaces and its topology, fuzzy normed and Banach spaces, linear operators, fundamental theorems (open mapping and closed graph), applications of contractions and fixed point theory, approximation theory and best proximity theory, fuzzy metric type space, topology and applications.